Years ago, I had a dog that was too dumb to train. She learned shake and almost mastered sit, but that was about it. She was an outside dog, so the housetraining wasn't that big a deal, but she never really could learn any other commands. She was a lovely solid white German Shepard, but she wasn't the brightest dog I ever had. To be fair, though, I think she had some mental disabilities. She was the victim of inbreeding, so there is no telling what went wrong.